6. The potential energy of a stretched membrane can be expressed as follows where T is the tension in the membrane, p is the pressure applied to the top of the membrane, the displacement of the membrane is uz = U3 (x, x), and the integrals are evaluated over the area of the membrane. S/ [(1/4 2 ) + (x 2 )" ] dx, d x - 2 1 A II = - [ pu A puz dxdx Assuming the membrane is supported along its edge (uz = 0 along the edge), use the principle of stationary potential energy to derive the governing equation and boundary conditions. The membrane described in this problem can be visualized as the head of a drum.